Math Problem Statement

Evaluate the following expression. Enter your answer as an integer or a simplified fraction. 64^{-4}

Solution

The expression you want to evaluate is 646^{-4}.

To evaluate this, recall that a negative exponent means taking the reciprocal of the base and then raising it to the positive exponent. In this case:

64=1646^{-4} = \frac{1}{6^4}

Now, calculate 646^4:

64=6×6×6×6=12966^4 = 6 \times 6 \times 6 \times 6 = 1296

So:

64=112966^{-4} = \frac{1}{1296}

Thus, the simplified result is:

64=112966^{-4} = \frac{1}{1296}

Would you like any more details or have any questions? Here are some related questions you might want to explore:

  1. What is 737^{-3}?
  2. How do you simplify 525^{-2}?
  3. What happens when you have a negative exponent with a fraction as the base?
  4. How would you evaluate 252^{-5}?
  5. What is the reciprocal of 939^3?

Tip: A negative exponent tells you to "flip" the base and make the exponent positive!

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents

Formulas

a^{-n} = 1 / a^n

Theorems

Negative Exponent Rule

Suitable Grade Level

Grades 6-8